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Magnitude and Phase of a transfer function

Hi would anyone mind telling me where I have gone wrong?

TF = (s+1)/(2s^2+4s+1)
(jw+1)/(-2w^2+4jw+1)
Magnitude for a frequency of 0.1 rad/s =
1/√((1-〖(2 * 0.01)^2〗^2+〖(4 * 0.01)〗^2 )
Thanks :smile:
(edited 6 years ago)
Original post by theelegantmango
Hi would anyone mind telling me where I have gone wrong?

TF = (s+1)/(2s^2+4s+1)
(jw+1)/(-2w^2+4jw+1)
Magnitude for a frequency of 0.1 rad/s =
1/√((1-〖(2 * 0.01)^2〗^2+〖(4 * 0.01)〗^2 )
Thanks :smile:


I'm not familiar with transfer functions. So, assuming all you're doing is substituting 0.1 for ω\omega and that j=−1j=\sqrt{-1}, and you had s=jωs=j\omega then we have:

jω+11−2ω2+4jω\displaystyle\frac{j \omega+1}{1-2\omega^2+4j\omega}

Magnitude =∣jω+11−2ω2+4jω∣\displaystyle=\left|\frac{j \omega+1}{1-2\omega^2+4j\omega}\right|

=∣jω+1∣∣1−2ω2+4jω∣\displaystyle=\frac{|j\omega+1|}{|1-2\omega^2+4j\omega|}

=ω2+1(1−2ω2)2+16ω2\displaystyle=\frac{\sqrt{\omega^2+1}}{\sqrt{(1-2\omega^2)^2+16\omega^2}}

So, it looks like your numerator is missing a ω2\omega^2 then square rooting, and the second part of the first term in your denominator should be −2×0.12-2\times 0.1^2
(edited 6 years ago)

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